DECISION THEORY: INTRODUCTION TO DECISION UNDER UNCERTAINTY

The course will emphasize the conceptual foundations of the theory, as well as the mathematical ones. Results will be proven in class when practical, at least in simple versions.

Parts I-IV describe classical theory. In passing, we will discuss deviations from the theory, newer theories, and the like, but these will not be the focus of attention.
Parts V-VI describe newer developments, which violate some of the classical assumptions. It will be argued that these deviations are note necessarily irrational. Thus, the cours does not directly deal with psychological biases or "mistakes".

The course is designed to be taught alongside the course given by Professor Abdellaoui, and these courses are complementary.
The course will have some overlap with the APE course on decision theory (given by Gilboa), but this will be kept to a minimum, so that it would make sense for a student to take both courses.

List of topics

1. Utility Theory: Choice functions and binary relations; representation of a binary relation by a utility
function; semi-orders; ordinal and cardinal utility

2. Subjective Probability: de Finetti's representation theorem

3. Decision under Risk: von Neumann-Morgenstern theorem

4. Decision under Uncertainty: Savage's theorem

5. Non-Additive Probabilities: Schmeidler's theoryem (Choquet Expected Utility)

6. Multiple Priors: Maxmin expected utility; the relationship to Choquet expected utility and cores of
convex games; alternative models

Requirements
There will be a final examination, as well as one or two midterm examinations. Homework assignments will be given as we go along, but will not be graded.

TEXTBOOKS
-Fishburn, P.C. Utilily Theory for Decision Making. John Wiley and Sons, 1970.
-Gilboa, I. Theory of Decision under Uncertainty. Cambridge University Press (Econometric Society
Monograph Series, n° 45), 2009.
-Kreps, D. Notes on the Theory of Choice. Westview Press: Underground Classics in Economics,
1988.
-Savage, J.L. The Foundations of Statistics. John Wiley and Sons, 1954/1972.

Dernière mise à jour : mardi 31 juillet 2012